Evaluate the definite integral. $\int^{2\pi}_{\pi}-\cos(x)\,dx = $
Explanation: First, use the cosine rule: $\begin{aligned}\int^{2\pi}_{\pi}-\cos(x)\,dx~&=~-\sin(x)\Bigg|^{2\pi}_{{\pi}}\end{aligned}$ Second, plug in the limits of integration: $(-{\sin(2\pi)})-(-{\sin(\pi)}) = 0-0 =0$. The answer: $\int^{2\pi}_{\pi}-\cos(x)\,dx~=~0$